My plant needs some boost

I have the plan in the photo attached which leaves on one of the branches are going down and dying, I am afraid that other branches will be touched. Is there anything I can do to stop that.
Should I cut the sick branch, where should I cut?

This appears to be the start of a fungal infection. The best course of action from here will be that the next time you water, you will replace 1/4 of that with peroxide. You should only need to do this once. It will kill off the infection while leaving your plant alone.